Three common mistakes in statistics and how to avoid them

class: center, middle, inverse, title-slide

.title[
# Three common mistakes in statistics and how to avoid them
]
.author[
### Elizabeth Pankratz
]
.institute[
### Department of Psychology<br>The University of Edinburgh
]

---

.pull-left[
## The mistake
]

.pull-right[
## How you'll avoid it
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3L562.7 256l-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z"/></svg>
**A common R programming mistake:**
Letting R treat all variables that consist of numbers as numeric.
]

.pull-right[
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M160 80c0-26.5 21.5-48 48-48h32c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H208c-26.5 0-48-21.5-48-48V80zM0 272c0-26.5 21.5-48 48-48H80c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V272zM368 96h32c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H368c-26.5 0-48-21.5-48-48V144c0-26.5 21.5-48 48-48z"/></svg> 
**An advanced statistical mistake:**
Modelling categorical, ordinal data as if it were numeric.
]

.pull-right[
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 384 512" style="height:1em;width:0.75em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M192 32c17.7 0 32 14.3 32 32V199.5l111.5-66.9c15.2-9.1 34.8-4.2 43.9 11s4.2 34.8-11 43.9L254.2 256l114.3 68.6c15.2 9.1 20.1 28.7 11 43.9s-28.7 20.1-43.9 11L224 312.5V448c0 17.7-14.3 32-32 32s-32-14.3-32-32V312.5L48.5 379.4c-15.2 9.1-34.8 4.2-43.9-11s-4.2-34.8 11-43.9L129.8 256 15.5 187.4c-15.2-9.1-20.1-28.7-11-43.9s28.7-20.1 43.9-11L160 199.5V64c0-17.7 14.3-32 32-32z"/></svg>
**A foundational statistical mistake:**
Interpreting a significant *p*-value as evidence that an effect exists.
]

.pull-right[
]

---
class: inverse, middle, center

# The data we'll use

---

## The SMARVUS dataset (Terry et al., 2023)

.center[SMARVUS = **S**tatistics and **M**athematics **A**nxieties and **R**elated **V**ariables in **U**niversity **S**tudents]

.pull-left[
A survey of *n* = 18,841 students (mostly Psychology UGs) from 35 countries.

Students rated their anxiety from 1 (no anxiety) to 5 (a great deal of anxiety) in scenarios like:

- Studying for a statistics test.

- Interpreting the meaning of a table in a journal article.

- **Going to ask my statistics teacher for individual help with material I am having difficulty understanding. → ** 
]

.pull-right[

]

---

## Why Likert scale ratings are not continuous numeric

.center[
![:scale 80%](data:image/png;base64,#imgs/rating-scale-0.png)
]

---
count:false

## Why Likert scale ratings are not continuous numeric

.center[
![:scale 80%](data:image/png;base64,#imgs/rating-scale-1.png)
]

---
count:false

## Why Likert scale ratings are not continuous numeric

.center[
![:scale 80%](data:image/png;base64,#imgs/rating-scale-2.png)
]

---
count:false

## Why Likert scale ratings are not continuous numeric

.center[
![:scale 80%](data:image/png;base64,#imgs/rating-scale-3.png)
]

---

## And yet...

.pull-left[
![](data:image/png;base64,#imgs/ReederEtAl2017-JML.png)

Reeder et al. (2017) in **Journal of Memory and Language.**

]

.pull-right[

![](data:image/png;base64,#imgs/ElazarEtAl2022-CogSci2.png)

Elazar et al. (2022) in **Cognitive Science.**

<br>

![](data:image/png;base64,#imgs/HarriganEtAl2022-Language.png)

Harrigan et al. (2022) in **Language.**

]

---

## R will keep numeric-looking data numeric

.pull-left[

``` r
head(anx, 3)
```

```
## # A tibble: 3 × 3
##   unique_id gender       rating
##   <chr>     <fct>         <dbl>
## 1 01057178  Male/Man          3
## 2 0300b5f2  Female/Woman      1
## 3 03f6503b  Female/Woman      3
```

]

.pull-right[

If we allow R's default behaviour, then we can do naughty things with categorical variables:

``` r
mean(anx$rating)
```

```
## [1] 2.868054
```

]

But if we **store these variables as factors,** the naughty things become impossible (yay!):

``` r
anx <- anx |> mutate(rating = factor(rating))

mean(anx$rating)
```

```
## [1] NA
```

---

.pull-left[
## The mistake
]

.pull-right[
## How you'll avoid it
]

.pull-right[
]

---
count:false

.pull-left[
## The mistake
]

.pull-right[
## How you'll avoid it
]

.pull-right[
When you know a variable is categorical, tell R that using `factor()`.
]

.pull-right[
]

---
class: inverse, middle, center

# Modelling an ordinal variable

### The .mono-white[polr()] express

---

## Model ordinal data with `polr()`

polr = **P**roportional **O**dds **L**ogistic **R**egression

``` r
library(MASS)        # MASS contains the polr() function

anx_fit1 <- polr(
  rating ~ 1,        # intercept-only model, to start
  data = anx, 
  Hess = TRUE,       # required if we want to use summary()
  method = 'probit'  # more on this in a moment
)
```

---

##  Model ordinal data with `polr()`

``` r
summary(anx_fit1)
```

```
## Call:
## polr(formula = rating ~ 1, data = anx, Hess = TRUE, method = "probit")
## 
## No coefficients
## 
## Intercepts:
##     Value    Std. Error t value 
## 1|2  -0.8420   0.0157   -53.7268
## 2|3  -0.1678   0.0138   -12.1462
## 3|4   0.3833   0.0141    27.1512
## 4|5   1.0339   0.0168    61.6193
## 
## Residual Deviance: 26596.28 
## AIC: 26604.28
```

---

## What do those `Intercepts` mean?

???

- imagine that there's some underlying continuous normal distribution of anxiety, assumed standard normal [show normal distrib]
- ppl with high anxiety are more likely to give high responses, ppl with low anxiety more likely to give low responses (could do emojis relating to anxiety: <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M464 256A208 208 0 1 0 48 256a208 208 0 1 0 416 0zM0 256a256 256 0 1 1 512 0A256 256 0 1 1 0 256zm177.6 62.1C192.8 334.5 218.8 352 256 352s63.2-17.5 78.4-33.9c9-9.7 24.2-10.4 33.9-1.4s10.4 24.2 1.4 33.9c-22 23.8-60 49.4-113.6 49.4s-91.7-25.5-113.6-49.4c-9-9.7-8.4-24.9 1.4-33.9s24.9-8.4 33.9 1.4zm40-89.3l0 0 0 0-.2-.2c-.2-.2-.4-.5-.7-.9c-.6-.8-1.6-2-2.8-3.4c-2.5-2.8-6-6.6-10.2-10.3c-8.8-7.8-18.8-14-27.7-14s-18.9 6.2-27.7 14c-4.2 3.7-7.7 7.5-10.2 10.3c-1.2 1.4-2.2 2.6-2.8 3.4c-.3 .4-.6 .7-.7 .9l-.2 .2 0 0 0 0 0 0c-2.1 2.8-5.7 3.9-8.9 2.8s-5.5-4.1-5.5-7.6c0-17.9 6.7-35.6 16.6-48.8c9.8-13 23.9-23.2 39.4-23.2s29.6 10.2 39.4 23.2c9.9 13.2 16.6 30.9 16.6 48.8c0 3.4-2.2 6.5-5.5 7.6s-6.9 0-8.9-2.8l0 0 0 0zm160 0l0 0-.2-.2c-.2-.2-.4-.5-.7-.9c-.6-.8-1.6-2-2.8-3.4c-2.5-2.8-6-6.6-10.2-10.3c-8.8-7.8-18.8-14-27.7-14s-18.9 6.2-27.7 14c-4.2 3.7-7.7 7.5-10.2 10.3c-1.2 1.4-2.2 2.6-2.8 3.4c-.3 .4-.6 .7-.7 .9l-.2 .2 0 0 0 0 0 0c-2.1 2.8-5.7 3.9-8.9 2.8s-5.5-4.1-5.5-7.6c0-17.9 6.7-35.6 16.6-48.8c9.8-13 23.9-23.2 39.4-23.2s29.6 10.2 39.4 23.2c9.9 13.2 16.6 30.9 16.6 48.8c0 3.4-2.2 6.5-5.5 7.6s-6.9 0-8.9-2.8l0 0 0 0 0 0z"/></svg>, <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:1em;width:1em;vertical-align:-0.125em;margin-left:auto;margin-right:auto;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M256 48a208 208 0 1 0 0 416 208 208 0 1 0 0-416zM512 256A256 256 0 1 1 0 256a256 256 0 1 1 512 0zM168 320c-13.3 0-24 10.7-24 24s10.7 24 24 24h8V320h-8zm40 48h32V320H208v48zm96 0V320H272v48h32zm32 0h8c13.3 0 24-10.7 24-24s-10.7-24-24-24h-8v48zM168 288H344c30.9 0 56 25.1 56 56s-25.1 56-56 56H168c-30.9 0-56-25.1-56-56s25.1-56 56-56zm-23.6-80a32 32 0 1 1 64 0 32 32 0 1 1 -64 0zm192-32a32 32 0 1 1 0 64 32 32 0 1 1 0-64z"/></svg>)
- so to estimate how different anxiety levels translate to different responses on the 1--5 scale, we draw thresholds on that distribution [add thresholds]
- ppl with anxiety in this bin will respond with 1, in this bin with 2, etc.
- and those thresholds, the cutpoints btwn ratings, are the intercepts.
- [show intercept estimates, put thoes same numbers on the thresholds]
- normal distribution assumption is from method = probit. other methods assume other underlying distributions, but the idea of thresholds is the same.

---
count: false

## What do those `Intercepts` mean?

---
count: false

## What do those `Intercepts` mean?

---
class: inverse, middle, center

# Stats anxiety and gender

---

#### How does a student's gender affect how they respond to "Going to ask my statistics teacher for individual help with material I am having difficulty understanding"?

.pull-left[

<img src="data:image/png;base64,#demo_files/figure-html/plot-gender-bars-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[

]

---

.center[

<img src="data:image/png;base64,#demo_files/figure-html/fem-normal-1.png" width="936" style="display: block; margin: auto;" />
]

---
count: false

---
count: false

---

``` r
anx_fit2 <- polr(
  rating ~ gender,
  data = anx,
  method = 'probit',
  Hess = TRUE
)
summary(anx_fit2)
```

```
## Coefficients:
##                        Value Std. Error t value
## genderMale/Man       -0.3280    0.03015 -10.880
## genderAnother Gender  0.4846    0.11992   4.041
## 
## Intercepts:
##     Value    Std. Error t value 
## 1|2  -0.9045   0.0169   -53.5402
## 2|3  -0.2246   0.0150   -14.9847
## 3|4   0.3318   0.0151    21.9158
## 4|5   0.9889   0.0176    56.2958
```

---

.pull-left[
## The mistake
]
.pull-right[
## How you'll avoid it
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3L562.7 256l-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z"/></svg>
**A common R programming mistake:**
Letting R treat all variables that consist of numbers as numeric.
]
.pull-right[
When you know a variable is categorical, tell R that using `factor()`.
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M160 80c0-26.5 21.5-48 48-48h32c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H208c-26.5 0-48-21.5-48-48V80zM0 272c0-26.5 21.5-48 48-48H80c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V272zM368 96h32c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H368c-26.5 0-48-21.5-48-48V144c0-26.5 21.5-48 48-48z"/></svg> 
**An advanced statistical mistake:**
Modelling categorical, ordinal data as if it were numeric.
]
.pull-right[
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 384 512" style="height:1em;width:0.75em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M192 32c17.7 0 32 14.3 32 32V199.5l111.5-66.9c15.2-9.1 34.8-4.2 43.9 11s4.2 34.8-11 43.9L254.2 256l114.3 68.6c15.2 9.1 20.1 28.7 11 43.9s-28.7 20.1-43.9 11L224 312.5V448c0 17.7-14.3 32-32 32s-32-14.3-32-32V312.5L48.5 379.4c-15.2 9.1-34.8 4.2-43.9-11s-4.2-34.8 11-43.9L129.8 256 15.5 187.4c-15.2-9.1-20.1-28.7-11-43.9s28.7-20.1 43.9-11L160 199.5V64c0-17.7 14.3-32 32-32z"/></svg>
**A foundational statistical mistake:**
Interpreting a significant *p*-value as evidence that an effect exists.
]
.pull-right[
]

---
count: false

.pull-left[
## The mistake
]
.pull-right[
## How you'll avoid it
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3L562.7 256l-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z"/></svg>
**A common R programming mistake:**
Letting R treat all variables that consist of numbers as numeric.
]
.pull-right[
When you know a variable is categorical, tell R that using `factor()`.
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M160 80c0-26.5 21.5-48 48-48h32c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H208c-26.5 0-48-21.5-48-48V80zM0 272c0-26.5 21.5-48 48-48H80c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V272zM368 96h32c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H368c-26.5 0-48-21.5-48-48V144c0-26.5 21.5-48 48-48z"/></svg> 
**An advanced statistical mistake:**
Modelling categorical, ordinal data as if it were numeric.
]
.pull-right[
Apply and interpret ordinal regression models (e.g., `polr()` from `MASS`).
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 384 512" style="height:1em;width:0.75em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M192 32c17.7 0 32 14.3 32 32V199.5l111.5-66.9c15.2-9.1 34.8-4.2 43.9 11s4.2 34.8-11 43.9L254.2 256l114.3 68.6c15.2 9.1 20.1 28.7 11 43.9s-28.7 20.1-43.9 11L224 312.5V448c0 17.7-14.3 32-32 32s-32-14.3-32-32V312.5L48.5 379.4c-15.2 9.1-34.8 4.2-43.9-11s-4.2-34.8 11-43.9L129.8 256 15.5 187.4c-15.2-9.1-20.1-28.7-11-43.9s28.7-20.1 43.9-11L160 199.5V64c0-17.7 14.3-32 32-32z"/></svg>
**A foundational statistical mistake:**
Interpreting a significant *p*-value as evidence that an effect exists.
]
.pull-right[
]

---
class: inverse, middle, center

# Interpreting *p*-values

---

## Are the effects of `gender` significant?

```
## Coefficients:
##                        Value Std. Error t value
## genderMale/Man       -0.3280    0.03015 -10.880
## genderAnother Gender  0.4846    0.11992   4.041
```

No *p*-values in the model summary.

But it's common practice to compare these *t*-values to a standard normal distribution.

``` r
pnorm(abs(-10.880), lower.tail = FALSE) * 2
```

```
## [1] 1.43563e-27
```

``` r
pnorm(abs(  4.041), lower.tail = FALSE) * 2
```

```
## [1] 5.322376e-05
```

???

Since both *p*-values are below 0.05:

- we CAN reject the null hypothesis that gender has no effect on ratings.
- **we CANNOT conclude that there really is an effect of gender.**

---

### Why don't significant *p*-values mean an effect exists?

Because we can also get significant *p*-values when there really is *no* effect.

.pull-left[
No difference in the true population:

<img src="data:image/png;base64,#demo_files/figure-html/true-skew-probdist-1.png" width="504" style="display: block; margin: auto;" />
]

.pull-right[
A possible random sample (*n* = 50 per group):

]

---

### Why don't significant *p*-values mean an effect exists?

``` r
sim_fit <- polr(rating ~ group, data = simdat, method = 'probit', Hess = TRUE)
summary(sim_fit)  
```

```
## Coefficients:
##                Value Std. Error t value
## groupGroup B -0.4479     0.2229  -2.009
```

<br>

``` r
pnorm(abs(-2.009), lower.tail = FALSE) * 2
```

```
## [1] 0.04453713
```

So *p* is below 0.05, but in the true population, Group A and Group B were identical!

---

.pull-left[
## The mistake
]
.pull-right[
## How you'll avoid it
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3L562.7 256l-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z"/></svg>
**A common R programming mistake:**
Letting R treat all variables that consist of numbers as numeric.
]
.pull-right[
When you know a variable is categorical, tell R that using `factor()`.
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M160 80c0-26.5 21.5-48 48-48h32c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H208c-26.5 0-48-21.5-48-48V80zM0 272c0-26.5 21.5-48 48-48H80c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V272zM368 96h32c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H368c-26.5 0-48-21.5-48-48V144c0-26.5 21.5-48 48-48z"/></svg> 
**An advanced statistical mistake:**
Modelling categorical, ordinal data as if it were numeric.
]
.pull-right[
Apply and interpret ordinal regression models (e.g., `polr()` from `MASS`).
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 384 512" style="height:1em;width:0.75em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M192 32c17.7 0 32 14.3 32 32V199.5l111.5-66.9c15.2-9.1 34.8-4.2 43.9 11s4.2 34.8-11 43.9L254.2 256l114.3 68.6c15.2 9.1 20.1 28.7 11 43.9s-28.7 20.1-43.9 11L224 312.5V448c0 17.7-14.3 32-32 32s-32-14.3-32-32V312.5L48.5 379.4c-15.2 9.1-34.8 4.2-43.9-11s-4.2-34.8 11-43.9L129.8 256 15.5 187.4c-15.2-9.1-20.1-28.7-11-43.9s28.7-20.1 43.9-11L160 199.5V64c0-17.7 14.3-32 32-32z"/></svg>
**A foundational statistical mistake:**
Interpreting a significant *p*-value as evidence that an effect exists.
]
.pull-right[
]

---
count:false

.pull-left[
## The mistake
]
.pull-right[
## How you'll avoid it
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 640 512" style="height:1em;width:1.25em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M392.8 1.2c-17-4.9-34.7 5-39.6 22l-128 448c-4.9 17 5 34.7 22 39.6s34.7-5 39.6-22l128-448c4.9-17-5-34.7-22-39.6zm80.6 120.1c-12.5 12.5-12.5 32.8 0 45.3L562.7 256l-89.4 89.4c-12.5 12.5-12.5 32.8 0 45.3s32.8 12.5 45.3 0l112-112c12.5-12.5 12.5-32.8 0-45.3l-112-112c-12.5-12.5-32.8-12.5-45.3 0zm-306.7 0c-12.5-12.5-32.8-12.5-45.3 0l-112 112c-12.5 12.5-12.5 32.8 0 45.3l112 112c12.5 12.5 32.8 12.5 45.3 0s12.5-32.8 0-45.3L77.3 256l89.4-89.4c12.5-12.5 12.5-32.8 0-45.3z"/></svg>
**A common R programming mistake:**
Letting R treat all variables that consist of numbers as numeric.
]
.pull-right[
When you know a variable is categorical, tell R that using `factor()`.
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 448 512" style="height:1em;width:0.88em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M160 80c0-26.5 21.5-48 48-48h32c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H208c-26.5 0-48-21.5-48-48V80zM0 272c0-26.5 21.5-48 48-48H80c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V272zM368 96h32c26.5 0 48 21.5 48 48V432c0 26.5-21.5 48-48 48H368c-26.5 0-48-21.5-48-48V144c0-26.5 21.5-48 48-48z"/></svg> 
**An advanced statistical mistake:**
Modelling categorical, ordinal data as if it were numeric.
]
.pull-right[
Apply and interpret ordinal regression models (e.g., `polr()` from `MASS`).
]

.pull-left[
<svg aria-hidden="true" role="img" viewBox="0 0 384 512" style="height:1em;width:0.75em;vertical-align:-0.125em;margin-left:auto;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M192 32c17.7 0 32 14.3 32 32V199.5l111.5-66.9c15.2-9.1 34.8-4.2 43.9 11s4.2 34.8-11 43.9L254.2 256l114.3 68.6c15.2 9.1 20.1 28.7 11 43.9s-28.7 20.1-43.9 11L224 312.5V448c0 17.7-14.3 32-32 32s-32-14.3-32-32V312.5L48.5 379.4c-15.2 9.1-34.8 4.2-43.9-11s-4.2-34.8 11-43.9L129.8 256 15.5 187.4c-15.2-9.1-20.1-28.7-11-43.9s28.7-20.1 43.9-11L160 199.5V64c0-17.7 14.3-32 32-32z"/></svg>
**A foundational statistical mistake:**
Interpreting a significant *p*-value as evidence that an effect exists.
]
.pull-right[
Understand that significant *p*-values can arise even if no effect exists.
]

<br>

.center[**Thank you! <svg aria-hidden="true" role="img" viewBox="0 0 512 512" style="height:2em;width:2em;vertical-align:-0.5em;margin-left:0.2em;margin-right:0.2em;font-size:inherit;fill:currentColor;overflow:visible;position:relative;"><path d="M464 256A208 208 0 1 0 48 256a208 208 0 1 0 416 0zM0 256a256 256 0 1 1 512 0A256 256 0 1 1 0 256zm177.6 62.1C192.8 334.5 218.8 352 256 352s63.2-17.5 78.4-33.9c9-9.7 24.2-10.4 33.9-1.4s10.4 24.2 1.4 33.9c-22 23.8-60 49.4-113.6 49.4s-91.7-25.5-113.6-49.4c-9-9.7-8.4-24.9 1.4-33.9s24.9-8.4 33.9 1.4zm40-89.3l0 0 0 0-.2-.2c-.2-.2-.4-.5-.7-.9c-.6-.8-1.6-2-2.8-3.4c-2.5-2.8-6-6.6-10.2-10.3c-8.8-7.8-18.8-14-27.7-14s-18.9 6.2-27.7 14c-4.2 3.7-7.7 7.5-10.2 10.3c-1.2 1.4-2.2 2.6-2.8 3.4c-.3 .4-.6 .7-.7 .9l-.2 .2 0 0 0 0 0 0c-2.1 2.8-5.7 3.9-8.9 2.8s-5.5-4.1-5.5-7.6c0-17.9 6.7-35.6 16.6-48.8c9.8-13 23.9-23.2 39.4-23.2s29.6 10.2 39.4 23.2c9.9 13.2 16.6 30.9 16.6 48.8c0 3.4-2.2 6.5-5.5 7.6s-6.9 0-8.9-2.8l0 0 0 0zm160 0l0 0-.2-.2c-.2-.2-.4-.5-.7-.9c-.6-.8-1.6-2-2.8-3.4c-2.5-2.8-6-6.6-10.2-10.3c-8.8-7.8-18.8-14-27.7-14s-18.9 6.2-27.7 14c-4.2 3.7-7.7 7.5-10.2 10.3c-1.2 1.4-2.2 2.6-2.8 3.4c-.3 .4-.6 .7-.7 .9l-.2 .2 0 0 0 0 0 0c-2.1 2.8-5.7 3.9-8.9 2.8s-5.5-4.1-5.5-7.6c0-17.9 6.7-35.6 16.6-48.8c9.8-13 23.9-23.2 39.4-23.2s29.6 10.2 39.4 23.2c9.9 13.2 16.6 30.9 16.6 48.8c0 3.4-2.2 6.5-5.5 7.6s-6.9 0-8.9-2.8l0 0 0 0 0 0z"/></svg> Time for questions!**]

---
count: false

## References

Elazar, A., Alhama, R. G., Bogaerts, L., Siegelman, N., Baus, C., & Frost, R. (2022). When the "tabula" is anything but "rasa": What determines performance in the auditory statistical learning task? *Cognitive Science*, 46(2), e13102.

Harrigan, K., Hogoboom, A., & Cochrane, L. (2022). Furthering student engagement: Lab sections in introductory linguistics. *Language*, 98(4), e199–e223.

Reeder, P. A., Newport, E. L., & Aslin, R. N. (2017). Distributional learning of subcategories in an artificial grammar: Category generalization and subcategory restrictions. *Journal of Memory and Language*, 97, 17–29.

Terry, J., Ross, R. M., Nagy, T., Salgado, M., Garrido-Vásquez, P., Sarfo, J. O., Cooper, S., Buttner, A. C., Lima, T. J. S., Öztürk, İ., Akay, N., Santos, F. H., Artemenko, C., Copping, L. T., Elsherif, M. M., Milovanović, I., Cribbie, R. A., Drushlyak, M. G., Swainston, K., … Field, A. P. (2023). Data from an International Multi-Centre Study of Statistics and Mathematics Anxieties and Related Variables in University Students (the SMARVUS Dataset). *Journal of Open Psychology Data*, 11(1), 8.

---
count: false

## Helpful resources

- Jamieson's (2004) paper _[Likert scales: How to (ab)use them](https://onlinelibrary.wiley.com/doi/10.1111/j.1365-2929.2004.02012.x)_

- UCLA Statistical Methods and Data Analytics's web page _[Ordinal Logistic Regression](https://stats.oarc.ucla.edu/r/dae/ordinal-logistic-regression/)_

- A. Solomon Kurz' (2021) blog post _[Notes on the Bayesian cumulative probit](https://stats.oarc.ucla.edu/r/dae/ordinal-logistic-regression/)_

- Gelman & Hill's (2007) book _[Data Analysis Using Regression and Multilevel/Hierarchical Models](https://www.cambridge.org/highereducation/books/data-analysis-using-regression-and-multilevel-hierarchical-models/32A29531C7FD730C3A68951A17C9D983)_